SPH3U�Circuit Analysis with �Kirchhoff’s Voltage and Current Laws

Reviewing Terms

Series Circuits

• In series circuits, current can only take ____ path.
• The amount of current is the ____________in a series circuit.

Resistance in Series

• Each resistance in a series circuit adds to the _______________of the circuit.

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R_total = R₁ + R₂ + R₃...

Resistance in Series

• Light bulbs, resistors, motors, and heaters usually have ____________________than wires and batteries.

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Example #1

• How much current flows in a circuit with a 1.5-volt battery and three 1 ohm resistances (bulbs) in series?

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• Draw the circuit and show the formula/calculations on a separate sheet of lined paper!

Voltage in a Series Circuit

• Each separate resistance creates a ________ as the current passes through.
• As current flows along a series circuit, each type of resistor __________ some of the electrical energy into another form of energy.
• _________is used to calculate the voltage drop across each resistor.

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Kirchoff’s Voltage Law

Parallel Circuits

• In parallel circuits the current can take _________________________
• Because there are multiple branches, the current is not the same at all points in a parallel circuit.

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Parallel Circuits

• Sometimes these paths are called _________.
• The current through a branch is also called the ______________.
• When analyzing a parallel circuit, remember that the current always has to go somewhere.
• The total current in the circuit is _______________________________________.
• At every branch point the current flowing out must equal ________________________.
• This rule is known as ____________________.

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Kirchoff’s Current Law

Kirchoff’s Current Law

Voltage & Current in a Parallel Circuit

• In a parallel circuit the _________ is the same across each branch because each branch has a low resistance path back to the battery.
• The amount of ________ in each branch in a parallel circuit is not necessarily the same.
• The _______in each branch determines the current in that branch.

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Example #2

• Two bulbs with different resistances are connected in parallel to batteries with a total voltage of 3 volts.
• Calculate the total current supplied by the battery.

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• Draw the circuit and show the formula/calculations on a separate sheet of lined paper!

Advantages of Parallel Circuits

• Parallel circuits have two big advantages over series circuits:
• Each device in the circuit sees ___________________.
• Each device in the circuit may be __________________without stopping the current flowing to other devices in the circuit.

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Short Circuit

• A short circuit is a parallel path in a circuit with __________________________
• Short circuits can be made ___________ by connecting a wire between two other wires at different voltages.
• Short circuits are dangerous because they can draw _______________________.

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Resistance in Parallel Circuits

• Adding resistance in parallel provides ___________________, and more current flows.
• When more current flows for the same voltage, the total resistance of the circuit ____________.
• This happens because every new path in a parallel circuit allows more current to flow for the same voltage.

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Resistance in Parallel Circuits

Example #3

• A circuit contains a 2 ohm resistor and a 4 ohm resistor in parallel.

Calculate the total resistance of the circuit.

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• Draw the circuit and show the formula/calculations on a separate sheet of lined paper!

Analysis of Circuits

• All circuits work by manipulating ________________________
• The process of circuit analysis means figuring out what the currents and voltages in a circuit are, and also how they are _____________________.
• Three basic laws are the foundation of circuit analysis.

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The 3 Circuit Laws

Mixed or Combined Circuits

Key Question:

How do we analyze mixed (or network) circuits?

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Combined (Network) Circuits

• In many circuits, resistors are connected both in series and in parallel.
• Such a circuit is called a mixed circuit.
• There is no single formula for adding resistors in a network circuit.
• For very complex circuits, electrical engineers use computer programs that can rapidly solve equations for the circuit using Kirchhoff’s laws.

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Example #4

• Three bulbs, each with a resistance of 3Ω, are combined in the circuit in the diagram
• Three volts are applied to the circuit.
• Calculate the current in each of the bulbs.
• From your calculations, do you think all three bulbs will be equally bright?

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• Draw the circuit and show the formula/calculations on a separate sheet of lined paper!